Solve for $x$ and $y$ using elimination. $\begin{align*}-x+6y &= 3 \\ 4x-8y &= 4\end{align*}$
Explanation: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $4$ and the bottom equation by $3$ $\begin{align*}-4x+24y &= 12\\ 12x-24y &= 12\end{align*}$ Add the top and bottom equations. $8x = 24$ Divide both sides by $8$ and reduce as necessary. $x = 3$ Substitute $3$ for $x$ in the top equation. $- 3+6y = 3$ $-3+6y = 3$ $6y = 6$ $y = 1$ The solution is $\enspace x = 3, \enspace y = 1$.